Distribution of Maximum Earthquake Magnitudes in Future Time Intervals, Application to the Seismicity of Japan (1923-2007)

We modify the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. [2009] and apply it to the earthquake catalog of Japan (1923-2007). The method is based on the two main limit theorems of the theory of extreme values and on the derived duality between the Generalized Pareto Distribution (GPD) and Generalized Extreme Value distribution (GEV). We obtain the distribution of maximum earthquake magnitudes in future time intervals of arbitrary duration tau. This distribution can be characterized by its quantile Qq(tau) at any desirable statistical level q. The quantile Qq(tau) provides a much more stable and robust characteristic than the traditional absolute maximum magnitude Mmax (Mmax can be obtained as the limit of Qq(tau) as q tends to 1, and tau tends to infinity). The best estimates of the parameters governing the distribution of Qq(tay) for Japan (1923-2007) are the following: Form parameter for GEV = -0.1901 +- 0.0717; position parameter GEV(tau=200)= 6.3387 +- 0.0380; spread parameter for GEV(tau=200)= 0.5995 +- 0.0223; Q_0.90,GEV(tau=10)= 8.34 +- 0.32. We also estimate Qq(tau) for a set of q-values and future time periods in the range for tau between 1 and 50 years from 2007. For comparison, the absolute maximum estimate Mmax from GEV, which is equal to 9.57 +- 0.86, has a scatter more than twice that of the 90 percent quantile Q_{0.90,GEV}(tau=10) of the maximum magnitude over the next 10 years counted from 2007.Comment: 15 pages + 10 figure

New Approach to the Characterization of Mmax and of the Tail of the Distribution of Earthquake Magnitudes

We develop a new method for the statistical esitmation of the tail of the distribution of earthquake sizes recorded in the Worldwide Harvard catalog of seismic moments converted to mW-magnitudes (1977-2004 and 1977-2006). We show that using the set of maximum magnitudes (the set of T-maxima) in windows of duration T days provides a significant improvement over existing methods, in particular (i) by minimizing the negative impact of time-clustering of foreshock / main shock /aftershock sequences in the estimation of the tail of the magnitude distribution, and (ii) by providing via a simulation method reliable estimates of the biases in the Moment estimation procedure (which turns out to be more efficient than the Maximum Likelihood estimation). Using a simulation method, we have determined the optimal window size of the T-maxima to be T=500 days. We have estimated the following quantiles of the distribution of T-maxima of earthquake magnitudes for the whole period 1977-2006: Q_{0.16}(Mmax)=9.3, Q_{0.5}(Mmax)=9.7 and Q_{0.84}(Mmax)=10.3. Finally, we suggest two more stable statistical characterristics of the tail of the distribution of earthquake magnitudes: the quantile QT(q) of a high probability level q for the T-maxima, and the probability of exceedence for a high threshold magnitude. We obtained the following sample estimates for the global Harvard catalog: QT(q=0.98)=8.6 +- 0.2 and a probability for the T-maxima to exceed magnitude 8 equal to 0.13-0.20. The comparison between our estimates for the two periods 1977-2004 and 1977-2006, where the later period includes the great Sumatra earthquake, 24.12.2004, mW=9.0, confirms the instability of the estimation of the parameter Mmax and the stability of the two other estimates.Comment: 40 pages including 16 figures and 7 table

On variations of <i>fo</i>F2 and F-spread before strong earthquakes in Japan

International audienceThe statistical analysis of the variations of the dayly-mean frequency of the maximum ionospheric electron density foF2 is performed in connection with the occurrence of (more than 60) earthquakes with magnitudes M>6.0, depths hRfoF2 decreases before the earthquakes. One day before the shock the decrease amounts to about 5%. The statistical reliability of this phenomenon is obtained to be better than 0.95. Further, the variations of the occurrence probability of the turbulization of the F-layer (F spread) are investigated for (more than 260) earthquakes with M>5.5, hRfoF2 analysis, the Wolf number is less than 100 and the index SKp is smaller than 30, and in case of the F-spread study a Wolf number less than 80 and SKp smaller than 17 are chosen

The New Avalanche-Like Stochastic Model for Parameterization of Seismicity and Its Application to the South Sakhalin Island Seismicity

Seismic process is usually considered as an example of occurrence of the regime of self-organizing criticality (SOC). A model of seismic regime as an assemblage of randomly developing episodes of avalanche-like relaxation, occurring at a set of metastable subsystems, can be the alternative of such consideration. The model is defined by two parameters characterizing the scaling hierarchical structure of the geophysical medium and the degree of metastability of subsystems of this medium. In the assemblage, these two parameters define a model b-value. An advantage of such approach consists in a clear physical sense of parameters of the model. The application of the model for parameterization of the seismic regime of the south part of Sakhalin Island is considered. The models of space changeability of the scaling parameter and of temporal changeability of the parameter of metastability are constructed. The anomalous increase of the parameter of metastability was found in connection with the Gornozavodsk and Nevelsk earthquakes. At the present time, high values of this parameter occur in the area of the Poyasok Isthmus. This finding is examined in comparison with other indications of an increase in probability of occurrence of a strong earthquake in the South Sakhalin region

Multifractal Scaling of Thermally-Activated Rupture Processes

We propose a ``multifractal stress activation'' model combining thermally activated rupture and long memory stress relaxation, which predicts that seismic decay rates after mainshocks follow the Omori law $\sim 1/t^p$ with exponents $p$ linearly increasing with the magnitude $M_L$ of the mainshock and the inverse temperature. We carefully test this prediction on earthquake sequences in the Southern California Earthquake catalog: we find power law relaxations of seismic sequences triggered by mainshocks with exponents $p$ increasing with the mainshock magnitude by approximately $0.1-0.15$ for each magnitude unit increase, from $p(M_L=3) \approx 0.6$ to $p(M_L=7) \approx 1.1$, in good agreement with the prediction of the multifractal model.Comment: four pages and 2 figure

Algorithm and program for earthquake prediction based on the geological, geophysical, geomorphological and seismic data

By applying an improved  method of the Earth's crust classification, we develop an algorithm and build an earthquake prediction program using a combination of geological, geophysical, geomorphological and seismic data.This program includes a system of multiple windows with different functions, which can divide fault zones into the different segments by the maximum magnitude values Mmax. Using the constructed program, we carried out an earthquake prediction test for the Northwest Vietnam by a combination of geological, geophysical, geomorphological and seismic data. According to the received results, zoning maps of maximum earthquake prediction for the researched region has been established. The results show that the   areas, capable of generating earthquakes with Mmax = 6.5 - 6.8  are primarily concentrated along some major fault zones such as Lai Chau-Dien Bien, Son La, Song Ma, Song Da, Tuan Giao or near the intersection of these fault zones. The received results show a good accordance with the actual seismotectonic characteristics of the researched region.References Bui Van Duan, Nguyen Cong Thang, Nguyen Van Vuong, Pham Dinh Nguyen, 2013. The magnitude of the largest possible earthquake in the Muong La - Bac Yen fault zone. Journal of Sciences of the Earth 35, 53-49.Cao Dinh Trieu, 1999. Probable approach for long-term earthquake prediction in Vietnam based on the regulation of epicentral distribution. Journal of Geology, Series A (251), 14-21, Hanoi (in Vietnamese).Cao Dinh Trieu, Nguyen Huu Tuyen, Thai Anh Tuan, 2006. The correlation between the structure of the Earth’s crust and seismic activities in the Northwest region of Vietnam”. Journal of Sciences of the Earth, 28, 155-164, Hanoi (in Vietnamese).Cao Dinh Trieu, Ngo Thi Lu, Cao Xuan Bach et al., 2007. Prediction of maximum earthquake occurrence in Vietnam on the basis of crustal characteristics”. Proceedings of the 5th Vietnam’s Scientific Conference on Geophysics, 159-171, Science and Technics Publishing House, Hanoi (in Vietnamese).Dang Thanh Hai, Nguyen Duc Vinh, Cao Dinh Trieu, 2002. Long-term earthquake prediction in Lai Chau-Dien Bien region on the basis of time - magnitude model. Journal of Science and Technology, 40(4), 45-53, Hanoi (in Vietnamese).Dang Thanh Hai, 2003. Study on deep structures of the Earth’s crust and seismotectonic zoning in Northern Vietnam. Physics Ph.D. Thesis, 170p, Hanoi (in Vietnamese).Grishin A.P., 2001. The statistical model for predicting the occurrence time and magnitude of the earthquake”. Journal of Volcanology and Seismology (4), 60-65, Russian Academy of Sciences, Moscow. (in Russian).Grishin A.P., N.V. Kondoskaya, L.E. Levin, L.N. Solodinov, A.L. Petrov, O.M. Petrov, 2001. “Experiment of statistical prediction in Kaspi region (occurrence time, epicenter coordinate and magnitude value of the earthquake). 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Probabilistic Seismic Hazard Assessment Along the Southeastern Coast of Vietnam, Natural Hazards 24, 53-74.Nguyen Hong Phuong, Pham The Truyen, 2014. Probabilistic Seismic Hazard Assessment for the South Central Vietnam. Vietnam Journal of Earth Sciences 36, 451-461.Nguyen Dinh Xuyen (Project manager), Nguyen Ngoc Thuy et al., 1996. Database of earthquake mitigation measures in Vietnam. The final report of state-level independent project, Code KT-DL 92-07, 3 volumes, Institute of Geophysics, Hanoi (in Vietnamese).Nguyen Dinh Xuyen, 2002. Earthquake and earthquake hazard level. Internal document, Institute of Geophysics, Hanoi (in Vietnamese).Nguyen Dinh Xuyen, Pham Dinh Nguyen, Pham Quang Hung, Nguyen Anh Duong, 2003. Experiment of long-term earthquake prediction based on the mechanism of foreshock activities. Journal of Sciences of the Earth, 25(3), 193-200, Hanoi (in Vietnamese).Phan Trong Trinh, Ngo Van Liem, Nguyen Van Huong, Hoang Quang Vinh, Bui Van Thom, Bui Thi Thao, Mai Thanh Tan, Nguyen Hoang, 2012. Late Quaternary tectonics and seismotectonics along the Red River fault zone, North Vietnam. Earth-Science Reviews 114(3), 224-235.Phan Trong Trinh , Hoang Quang Vinh, Nguyen Van Huong, Ngo Van Liem, 2013. Active fault segmentation and seismic hazard in Hoa-Binh reservoir, Vietnam. Cent. Eur. J. Geosci. 5(2), 223-235.Pham Van Thuc and Kijko, A., 1985. Estimation of maximum magnitude and seismic hazard in Southeast Asia and Vietnam. Acta Geophys. Pol., XXX111 (4), 377-387.Pham Van Thuc, 2007. Seismology and earthquake in Vietnam. The monographs on natural resources and environment in Vietnam, Publishing House for Science and Technology, Vietnam Academy of Science and Technology, 378p (in Vietnamese).Reisner G.I., L.I. Ioganson, M.G. Reisner, Iu.E. Baranov, 1993. Characteristic classification of the Earth’s crust and the modern geological process. Publishing House of Russian Academy of Sciences, Moscow, 210p (in Russian).Reisner G.I., L.I. Ioganson, 1996. The Extraregional Seismotectonic Method for the Assessment of Seismic Potential. Natural Hazards 14, 3-10 (Kluwer Academic Publishers, printed in the Netherlands).Tran Thi My Thanh, 2002. Assessment of seismic hazard in Vietnam and adjacent regions. Physics Ph.D. Thesis, 161 pages, Hanoi (in Vietnamese).Vu Thi Hoan, Ngo Thi Lu, M.V. Rodkin, Tran Viet Phuong, 2014. Application of the generalized extreme value distribution to study the seismicity of the Southeast Asian. Journal of Geology. Series A, 341-345. Hanoi. 

О ВОЗМОЖНЫХ РЕАЛИЗАЦИЯХ ЗАКОНА РАСПРЕДЕЛЕНИЯ РЕДКИХ СИЛЬНЕЙШИХ ЗЕМЛЕТРЯСЕНИЙ

Assessment of long-term seismic hazard is critically dependent on the behavior of tail of the distribution function of rare strongest earthquakes. Analyses of empirical data cannot however yield the credible solution of this problem because the instrumental catalogs of earthquake are available only for a rather short time intervals, and the uncertainty in estimations of magnitude of paleoearthquakes is high. From the available data, it was possible only to propose a number of alternative models characterizing the distribution of rare strongest earthquakes. There are the following models: the model based on theGuttenberg – Richter law suggested to be valid until a maximum possible seismic event (Мmах), models of 'bend down' of earthquake recurrence curve, and the characteristic earthquakes model. We discuss these models from the general physical concepts supported by the theory of extreme values (with reference to the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD) and the multiplicative cascade model of seismic regime. In terms of the multiplicative cascade model, seismic regime is treated as a large number of episodes of avalanche-type relaxation of metastable states which take place in a set of metastable sub-systems.The model of magnitude-unlimited continuation of the Guttenberg – Richter law is invalid from the physical point of view because it corresponds to an infinite mean value of seismic energy and infinite capacity of the process generating seismicity. A model of an abrupt cut of this law by a maximum possible event, Мmах is not fully logical either.A model with the 'bend-down' of earthquake recurrence curve can ensure both continuity of the distribution law and finiteness of seismic energy value. Results of studies with the use of the theory of extreme values provide a convincing support to the model of 'bend-down' of earthquakes’ recurrence curve. Moreover they testify also that the 'bend-down' is described by the finite distribution law, i.e. the bend-down occurs more efficiently than it is envisaged in the commonly used model developed by Y. Kagan (which treats the bend-dawn as an exponential decay law). However, despite the finiteness of the distribution law, density of magnitudes decline quite slowly in the area close to the maximum possible Мmах event as (Мmах – M)n, where n varies in the range between 4 and 6 in the majority of cases. As a result Мmах value can be estimated only with a large error. In rare cases, if the space-and-time area under study contains higher number of strongest earthquakes, the empirical distribution law becomes close to the exponential law; in this case n value is quite high, and Мmах values becomes unstable and tend to infinite growth.In our study, the distribution law of strongest earthquakes was investigated by the methods based on the extreme values theory (world data and several regional catalogues were examined), and the results of calculation do not reveal cases of  occurrence of characteristic events. However, such a seismic regime was revealed in a number of cases from paleoseismicity data and from some instrumental regional catalogues. Conditions providing for the occurrence of characteristic earthquakes are studied here using the multiplicative cascade model. According to [Rodkin, 2011], this model provides the simulation of all known regularities of seismic regime, such as a decrease in b-value in the vicinity of strong earthquakes, development of aftershock power cascade, and existence of seismic cycle and foreshock activity. This article considers an extension of the cascade model by adding of non-linear members in the kinetic cascade equation in order to describe effects of the 'bend-down' of the earthquake recurrence curve and the characteristic earthquakes occurrence. It is shown that in terms of the multiplicative cascade model, the occurrence of characteristic earthquakes is connected with development of the nonlinear positive feedback between the size of the current rupture zone and the rate of its further growth.The modelling results are compared with data on seismicity of the South-Eastern Asia, which suggest that the regime providing the occurrence of characteristic earthquakes appears to be typical of the seismic regime of subduction zones (while it is not observed outside such zones). It is concluded that the non-linear positive feedback that controls the possibility of occurrence of characteristic earthquakes may be caused with the presence of deep fluids of increased concentration in the subduction zones. Принципиальное значение для оценки долгосрочной сейсмической опасности имеет поведение хвоста функции распределения редких сильнейших землетрясений. Краткость инструментальных каталогов землетрясений и большая погрешность определения магнитуд палеоземлетрясений не дают возможности надежно исследовать этот вопрос на основе эмпирических данных. На основе таких данных оказалось возможным только сформулировать несколько альтернативных моделей распределения редких сильнейших землетрясений. Наиболее распространенными моделями являются следующие: модель продолжения выполнимости обычного закона Гутенберга – Рихтера вплоть до некоторого максимально возможного события Мmах, модели с загибом вниз графика повторяемости землетрясений, модель реализации характеристических землетрясений. В статье эти модели анализируются на основе общих физических соображений, теоретических представлений, следующих из теории экстремальных значений (на основе использования Обобщенного распределения максимальных значений (GEV) и Обобщенного распределения Парето (GPD), и модели описания сейсмического режима мультипликативным каскадом. Последняя модель трактует сейсмический режим как совокупность эпизодов лавинообразной реализации (релаксации) метастабильных состояний, протекающих на множестве метастабильных подсистем.Модель неограниченного по магнитуде продолжения обычного закона Гуттенберга – Рихтера заведомо неточна, так как отвечает бесконечным значениям величин сейсмической энергии и мощности сеймогенерирующего процесса. При этом модель резкого обрезания этого закона некоторым максимально возможным событием Мmах также не вполне логична. Модель с загибом вниз графика повторяемости землетрясений позволяет обеспечить как непрерывность закона распределения, так и конечность величин сейсмической энергии. Результаты применения теории экстремальных значений весомо подкрепляют модель загиба вниз графика повторяемости. При этом выявляется, что загиб описывается конечным законом распределения, то есть оказывается более быстрым, чем предполагается в рамках широко распространенной модели Я. Кагана (отвечающей экспоненциальному закону убывания). Однако, несмотря на конечность закона распределения, плотность распределения магнитуд М в области максимально возможного события Мmах убывает достаточно медленно, как (Мmах – M)n, где n варьируется в большинстве случаев в диапазоне от 4 до 6. Отсюда следует, что величина Мmах может быть оценена обычно только с большой погрешностью. Изредка, если в исследуемой пространственно-временной области оказывается повышенное число сильнейших землетрясений, получаемый закон распределения приближается к экспоненциальному, при этом значения n становятся весьма большими, а значения Мmах существенно неустойчивыми.Проведенные расчеты закона распределения сильнейших землетрясений методами теории экстремальных значений (по мировым данным и ряду региональных каталогов) не выявили примеров реализации характеристических событий. Однако использование данных по палеосейсмичности и некоторые отдельные каталоги инструментальных данных свидетельствуют в пользу встречаемости такого сейсмического режима. Условия возникновения характеристических землетрясений исследованы в рамках модели мультипликативного каскада. Ранее было показано [Rodkin, 2011], что эта модель позволяет имитировать такие известные закономерности сейсмического режима, как уменьшение наклона графика повторяемости в окрестности сильных землетрясений, развитие афтершокового степенного каскада и предвестниковой активизации, а также существование сейсмического цикла. В статье обсуждается расширение схемы каскада добавлением нелинейных членов в кинетическое уравнение каскада с целью описания эффектов загиба вниз графика повторяемости землетрясений и возможности возникновения характеристических землетрясений. Показано, что в рамках модели мультипликативного каскада условием реализации характеристических землетрясений является развитие нелинейной цепи положительной обратной связи между размерами области сейсмического разрушения и скоростью ее дальнейшего роста. Результаты моделирования сопоставляются с данными по сейсмичности Юго-Восточной Азии, согласно которым режим возникновения характеристических землетрясений является типичным для сейсмического режима зон субдукции и не наблюдается вне этих зон. Делается вывод, что ответственная за реализацию характеристических землетрясений цепь нелинейной положительной обратной связи может быть обусловлена наличием в зонах субдукции резко повышенных концентраций глубинного флюида.